Synchronization in FitzHugh-Nagumo Neuronal Networks



Neuron Dynamics, Neuronal Networks, FitzHugh-Nagumo Neurons


Some of the most interesting neuroscience problems, fundamental to the field, are inherently mathematical. Central problems include understanding how cellular and network level mechanics of the peripheral and central nervous system coordinate to encode, process, and learn information, and how the Central Nervous System (CNS) is able to synchronize brain-wide neural activity. Answering these questions requires understanding how neuronal circuits react to stimuli and interact with one another to process information specific to their roles within a network. To simulate these intercellular dynamics, FitzHugh-Nagumo neurons were connected through incoming and outgoing voltage currents to form dynamic networks. External stimuli consisting of both excitatory and inhibitory signals were sent through the network. As the network’s connectivity coefficient increased, neurons began to synchronize. In some cases neuronal activity segregated and competed so that neither signal dominated the artificial network, underlining the importance of the relationship between signal and architecture in functional, biological circuits. Biological components which have been implicated in network synchronization, and how they could be mathematically implemented in future network simulations were discussed.

Author Biography

Valerie Kay Bullock, Florida State University

Valerie Bullock begins her senior year at Florida State University in Applied Mathematics following summer research with Dr. Nathan Kutz, University of Washington, Applied Mathematics. She intends completion of a Ph.D. in Applied Mathematics and is interested in information processing roles of neuron and glia dynamics in heterogeneous cellular networks.


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